Tham khảo tài liệu 'laser welding part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 154 Laser Welding Gr I L ATp2 Gr ---------5------ Rẻff 57 where g is gravitational acceleration p is the thermal expansion coefficient and LCR is the characteristics length. To understand the relative importance between surface tension force and buoyancy force the dimensionless number is defined by the ratio of surface tension Reynolds number and Grashof number and is expressed as 58 From the order of magnitude analysis the maximum velocity under surface tension force UST can be done assuming a boundary layer develops due to Marangoni shear stress and the maximum velocity occurs at a location approximately halfway between the heat source and weld pool edge DebRoy David 1995 ỞỴ dT U3 2 ST w1 2 ỔT dx 2u1. .2 x w 4 - p reff 59 dT where -j is average temperature gradient on the top of weld pool at the position of w 4. An order of magnitude analysis of the maximum velocity due to buoyancy driven flow is estimated as He et al. 2003 ug yl gPATp 60 where p is the depth of weld pool. The quantative estimation of various dimensionless numbers for present welding conditions is reported in Table 5 by using material data depicted in Table 2. It is obvious from the tabulated data of RST that the viscous force is less significant as compared to surface tension force. However the computed values of Gr indicate that viscous force is more significant as compared to buoyancy force. Overall the analysis on the quantative values of all driving force within molten pool indicates that surface tension force acts as the main driving force for the liquid metal movement in laser welding process. Hence the maximum magnitude of velocity is observed on the top of the weld pool Fig. 8 due to the surface tension force. Figure 12 describes the comparison of maximum magnitude of expected velocity between order of magnitude analyses and predicted from numerical model. The relatively small deviation between these values indicates that the numerical model predicts the velocity distribution
